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Some Integers written in a black board
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kunny
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#1
 Some Integers written in a black board
2009 Japan Mathematical Olympiad Finals, Problem 2
Let N be postive integer. Some integers are written in a black board and those satisfy the following conditions.

1. Any numbers written are integers which are from 1 to N.

2. More than one integer which is from 1 to N is written.

3. The sum of numbers written is even.

If we mark X to some numbers written and mark Y to all remaining numbers, then prove that we can set the sum of numbers marked X are equal to that of numbers marked Y.
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PostPosted: Sat Feb 21, 2009 6:12 pm
pbornsztein
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Wink What about N=10 and written numbers are 2,3,9?

Pierre.

PostPosted: Sat Feb 21, 2009 8:21 pm
Rijul saini
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#3
Hey there seems to be some typo in the question......i was also thinking that the question was wrong......and when i came across this thread the last post confirmed my doubts.......so can anyone change the question to one that is readily solvable....
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PostPosted: Sun Jun 07, 2009 6:29 am
kunny
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#4
Re: Some Integers written in a black board
2009 Japan Mathematical Olympiad Finals, Problem 2
Sorry for my poor English. How about this?


Let N be postive integer. Some integers are written in a blackboard. Suppose that :

1. The written number is all belong to 1,\ 2,\ \cdots N.

2. Each of integer of 1,\ 2,\ \cdots N is written at least one.

3. The sum of numbers written in the black board is even.

If we mark X to some numbers written and mark Y to all remaining numbers, then prove that we can set the sum of numbers marked X are equal to that of numbers marked Y.
_________________
Today's calculation of Integral Digest

PostPosted: Sun Jun 07, 2009 2:01 pm
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